Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×#1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C41 | D4 |
| commutator | C4 | C2×C16×C41 |
| Frattini, cosocle | C2×C16 | C22×C41 |
| socle | C2×C41 | C22⋊C16 |
| prime radical | #41×C41 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C41 ◁ C2×C16×C41 ◁ G | |
72 conjugacy classes of subgroups.
2296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#1401, C41×#13558, C41×#13647, … |
| maximal normal subgroup of | C2×C41×#1401, C41×#13558, C41×#13647, … |
| maximal quotient of | C41×#7335, C41×#7363, C41×D4⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 133);